Tuesday, July 31, 2018

"The Peculiar Math that Could Underly the Laws of Nature": how tuples generate string theory, and more

Wired Magazine has published several important articles on the way deep laws of mathematics drive physics and biology.

The most recent, July 28, is by Matalie Wolchover, and is titled “The Peculiar Math that Could Underly the Laws of Nature”.  It’s also in Quanta Magazine here

She is a mathematician from Waterloo University in Ontario, and has worked with Penn State on this issue.

Her argument reminds me of the progression to real variables to complex variable in graduate school in mathematics (in my case, at Kansas University in the 1960s). Complex gives us some beauty, like the Mandelbrot set;  and Liousville Theorem may explain why the Universe seems infinite from any point.

From complex variables you get to quaternions, and from those to octonions. 

Now quaternion field theory doesn’t follow the commutative law, and octernions don’t even follow the associate law.  I remember giving my students quiz questions on those laws when I worked as a graduate student assistant instructor (many of them couldn’t restate the concepts).

From octonion math you can deduce string theory, the 11 dimensions and why time behaves the way it does.  You can also explain the fundamental forces in physics, maybe, and build quarks.
I hope you can’t build a contagious strangelet to make gray goo.

I could wonder, though, wouldn’t these tuples behave like vector spaces? Remember linear independence?

Here are a couple other big Wired (paywall) stories on theoretical mathematics. 

John Rennie on July1, 2018 writes “This Mutation Math Shows How Life Keeps on Evolving.”

And on Dec. 17, 2017, Kevin Hartnett published, “Secret Link Discovered Between Pure Math and Physics” , the work of Minhyong Kim at the University of Oxford, getting into “series of spaces”.

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